Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, p. 923-937

In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under weaker conditions on the triangulations than quasiuniformity. In the two-dimensional case, the bound for the resolvent contains a logarithmic factor.

DOI : https://doi.org/10.1051/m2an:2006040
Classification:  65M06,  65M12,  65M60
Keywords: resolvent estimates, stability, smoothing, maximum-norm, elliptic, parabolic, finite elements, nonquasiuniform triangulations
@article{M2AN_2006__40_5_923_0,
     author = {Bakaev, Nikolai Yu. and Crouzeix, Michel and Thom\'ee, Vidar},
     title = {Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {5},
     year = {2006},
     pages = {923-937},
     doi = {10.1051/m2an:2006040},
     zbl = {1116.65108},
     mrnumber = {2293252},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2006__40_5_923_0}
}
Bakaev, Nikolai Yu.; Crouzeix, Michel; Thomée, Vidar. Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, pp. 923-937. doi : 10.1051/m2an:2006040. http://www.numdam.org/item/M2AN_2006__40_5_923_0/

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